1. Multiples Waveform Inversion
Dongliang Zhang and Gerard Schuster
King Abdullah University of Science and Technology
12/06/2013

2. Outline Motivation Theory Numerical Example Conclusions
Multiples contain more information
Theory
Algorithm of MWI and generation of multiples
Numerical Example
Test Marmousi model
Conclusions

3. Outline Motivation Theory Numerical Example Conclusions
Multiples contain more information
Theory
Algorithm of MWI and generation of multiples
Numerical Example
Test Marmousi model
Conclusions

4. Motivation Multiples : wider coverage, denser illumination multiples
primary
Multiples : wider coverage, denser illumination
FWI
MWI

5. Recorded data (primary + multiples)
Motivation
Multiples waveform inversion vs full waveform inversion
Source wavefield
Receiver wavefield
FWI
Impulsive wavelet
Recorded data
MWI
Recorded data (P+M)
Multiples (M)
Recorded data (primary + multiples)
Impulsive wavelet
Recorded data
multiples
Natural source

6. Outline Motivation Theory Numerical Example Conclusions
Multiples contain more information
Theory
Algorithm of MWI and generation of multiples
Numerical Example
Test Marmousi model
Conclusions

7. Theory Algorithm of MWI 1. Misfit function
2. Gradient of data residual
Multiples RTM

8. Algorithm of MWI Forward propagation Back propagation
3. Update velocity/slowness

9. MWI Workflow Calculate multiples to get the multiples residual
Multiples RTM to get
gradient of misfit function
Update the velocity
Number of iterations >N No
Yes
Stop

10. Generate Multiples Mr = (Pd+Md ) +Mr - (Pd+Md) Step 1 Pd+Md Mr Step 2
direct propagation
Pd+Md
Line source
(P +M)
heterogeneous Mr
reflected propagation
Step 2
direct propagation
homogeneous
Line source
(P +M)
Pd+Md
heterogeneous
homogeneous
Step 3
Mr = (Pd+Md ) +Mr - (Pd+Md)

11. Example water homogeneous (Pd+Md)+Mr (Pd+Md) Mr (multiples)
Virtual Source (P+M)
Example
T (s)
Z (km) 0
water homogeneous
X (km)
T (s)
(Pd+Md)+Mr
X (km)
(Pd+Md)
X (km)
Mr (multiples)

12. Conventional migration
Gradient of MWI
Multiples residual
Recorded data
Impulsive wavelet
Data residual
Multiples migration
Conventional migration
Yike Liu (2011)

13. Outline Motivation Theory Numerical Example Conclusions
Multiples contain more information
Theory
Algorithm of MWI and generation of multiples
Numerical Example
Test Marmousi model
Conclusions

14. Numerical Example True Velocity Model Initial Velocity Model
km/s
Z (km)
Z (km)
km/s
Initial Velocity Model
X (km)

15. Numerical Example Tomogram of FWI Tomogram of MWI 2 Z (km) 0
km/s
Z (km)
Tomogram of MWI
Z (km)
X (km)
km/s

16. Numerical Example
True
True
FWI
FWI
MWI
MWI

17. Numerical Example
RTM Image Using FWI Tomogram
Z (km)
X (km)

18. Numerical Example
RTM Image Using MWI Tomogram
Z (km)
X (km)

19. Numerical Example
Common Image Gather Using FWI Tomogram

20. Numerical Example
Common Image Gather Using MWI Tomogram

21. Numerical Example FWI MWI FWI MWI
Data Residual
Res (%)
Convergence of MWI is faster than that of FWI
FWI
MWI
Iterations
Res (%)
Model Residual
FWI
MWI
MWI is more accurate than FWI

22. Numerical Example FWI Gradient for One Shot MWI Gradient for One Shot
X (km)
MWI Gradient for One Shot

23. Outline Motivation Theory Numerical Example Conclusions
Multiples contain more information
Theory
Algorithm of MWI and generation of multiples
Numerical Example
Test Marmousi model
Conclusions

24. Conclusions Source wavelet is not required Illuminations are denser
MWI converge faster than FWI in test on Marmousi model
Tomogram of MWI is better than that of FWI in test on Marmousi model
FWI
MWI
FWI
MWI

25. Limitations: Dip anglevs
Future work:
P+M FWI
P+M MVA

26. Thank you!